2009/02/08 by Izu Vaisman, Vaisman, Izu
Biochemistry, Genetics and Molecular Biology · Mathematics · #53C12 #53D17 #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Sphingolipid Metabolism and Signaling #Symplectic Geometry (math.SG) #math.DG #math.SG #msc:53C12 #msc:53D17
paper · pdf · doi:10.48550/arxiv.0902.1296
LaTex, 28 pages, contains additional results
openalex publication_date 2009/02/08 · arxiv created 2009/11/23 · arxiv updated 2009/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
If A is a Lie algebroid over a foliated manifold (M,F), a foliation of A is a Lie subalgebroid B with anchor image TF and such that A/B is locally equivalent with Lie algebroids over the slice manifolds of F. We give several examples and, for foliated Lie algebroids, we discuss the following subjects: the dual Poisson structure and Vaintrob's super-vector field, cohomology and deformations of the foliation, integration to a Lie groupoid. In the last section, we define a corresponding notion of a foliation of a Courant algebroid A as a bracket-closed, isotropic subbundle B with anchor image TF and such that B^⊥/B is locally equivalent with Courant algebroids over the slice manifolds of F. Examples that motivate the definition are given.